What is (a-b)/(asqrt(b)-b\sqrt{a)} ?

The solution to (a-b)/(asqrt(b)-b\sqrt{a)} is (asqrt(b)+bsqrt(a))/(ab)

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simplify (a-b)/(asqrt(b)-b\sqrt{a)}

simplify

\frac{a - b}{a b - b a}

\frac{a b + b a}{ab}

Solution steps

\frac{a - b}{a b - b a}

Multiply by the conjugate

\frac{a b + b a}{a b + b a}

= \frac{( a - b ) ( a b + b a )}{( a b - b a ) ( a b + b a )}

(a b - b a) (a b + b a) = a^{2} b - a b^{2}

= \frac{( a - b ) ( a b + b a )}{a ^{2} b - a b ^{2}}

Factor

a^{2} b - a b^{2} : ba (a - b)

= \frac{( a - b ) ( a b + b a )}{ba ( a - b )}

Cancel the common factor:

a - b

= \frac{a b + b a}{ab}

12 + 4

17 - 6

20 - 4

3 (2 x - 2)

What is (a-b)/(asqrt(b)-b\sqrt{a)} ?
The solution to (a-b)/(asqrt(b)-b\sqrt{a)} is (asqrt(b)+bsqrt(a))/(ab)